This work investigates real-time monitoring of extrusion-induced degradation in different grades of PLA across a range of process conditions and machine set-ups. Data on machine settings together with in-process sensor data, including temperature, pressure, and near-infrared (NIR) spectra, are used as inputs to predict the molecular weight and mechanical properties of the product. Many soft sensor approaches based on complex spectral data are essentially 'black-box' in nature, which can limit industrial acceptability. Hence, the focus here is on identifying an optimal approach to developing interpretable models while achieving high predictive accuracy and robustness across different process settings. The performance of a Recursive Feature Elimination (RFE) approach was compared to more common dimension reduction and regression approaches including Partial Least Squares (PLS), iterative PLS (i-PLS), Principal Component Regression (PCR), ridge regression, Least Absolute Shrinkage and Selection Operator (LASSO), and Random Forest (RF). It is shown that for medical-grade PLA processed under moisture-controlled conditions, accurate prediction of molecular weight is possible over a wide range of process conditions and different machine settings (different nozzle types for downstream fibre spinning) with an RFE-RF algorithm. Similarly, for the prediction of yield stress, RFE-RF achieved excellent predictive performance, outperforming the other approaches in terms of simplicity, interpretability, and accuracy. The features selected by the RFE model provide important insights to the process. It was found that change in molecular weight was not an important factor affecting the mechanical properties of the PLA, which is primarily related to the pressure and temperature at the latter stages of the extrusion process. The temperature at the extruder exit was also the most important predictor of degradation of the polymer molecular weight, highlighting the importance of accurate melt temperature control in the process. RFE not only outperforms more established methods as a soft sensor method, but also has significant advantages in terms of computational efficiency, simplicity, and interpretability. RFE-based soft sensors are promising for better quality control in processing thermally sensitive polymers such as PLA, in particular demonstrating for the first time the ability to monitor molecular weight degradation during processing across various machine settings.